can someone help me with this question?
let z = F(x, y) = x^2 -y +1
b)find the functions g(x,y)= f( f(x,y) , y) and h(x,y)= f(x, (f(x,y) )
c)If f(x,y)= f(y,x) and x cannot equal to y
show that y= -x -1
a
f( f(x,y) , y)
= $\displaystyle (x^2 -y +1)^2 -y +1$
b
f(x,y)= f(y,x)
$\displaystyle => x^2 -y +1 = y^2 -x +1$
$\displaystyle = >x^2 - y^2 = y - x$
$\displaystyle => (x - y)(x + y) = y - x$
since x - y is not equal to zero, we can divide equation by x - y
$\displaystyle => x + y = -1$
$\displaystyle => y= -x -1 $